Start learning →

GRE Unit 1A1: Relations, Functions and Graphs — practice questions — page 2

Explore 73 free Unit 1A1: Relations, Functions and Graphs questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Unit 1A1: Relations, Functions and Graphs with Quill →

Unit 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 31–60 of 73.

How many perfect cubes are there from 1 to 1000 (both included)?Read the answer and worked solution →What is the cube of 12?Read the answer and worked solution →Which of the following numbers is NOT a perfect cube?Read the answer and worked solution →The units (one's) digit of (78)³ is:Read the answer and worked solution →Sum of the consecutive odd numbers needed to obtain 5³ = 125 is:Read the answer and worked solution →The smallest natural number by which 392 must be MULTIPLIED to make it a perfect cube is:Read the answer and worked solution →How many digits at MAXIMUM can the cube of a 2-digit number have?Read the answer and worked solution →A cuboid of plasticine has sides 5 cm, 2 cm and 5 cm. The MINIMUM number of such cuboids needed to form a perfect cube (without leftover) is:Read the answer and worked solution →Compute 25³ − 24³ using the pattern (n+1)³ − n³ = 1 + 3·n·(n+1):Read the answer and worked solution →Is 1188 a perfect cube? If not, the smallest natural number by which 1188 must be DIVIDED to make the quotient a perfect cube is:Read the answer and worked solution →A child stacks unit cubes (side 1 cm) to make a larger cube of side 4 cm. The number of unit cubes used is:Read the answer and worked solution →Which of the following statements is TRUE?Read the answer and worked solution →The cube of which number among the following is a 7-digit number?Read the answer and worked solution →Find the smallest perfect cube that is divisible by both 8 and 27.Read the answer and worked solution →arctan(x) is an _____ function (odd/even):Read the answer and worked solution →Maximum value of x² + (arcsin(x))² for x in [-1, 1]:Read the answer and worked solution →Which of the following sets of ordered pairs represents a function?Read the answer and worked solution →For finite sets, $n(A\times B)$ equals:Read the answer and worked solution →A relation $R$ on a set $A$ is reflexive if:Read the answer and worked solution →An equivalence relation is one that is:Read the answer and worked solution →A function $f:A\to B$ is one-one (injective) if:Read the answer and worked solution →A function $f:A\to B$ is onto (surjective) if:Read the answer and worked solution →A bijective function is one that is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = 2x + 3$ is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = x^2$ is:Read the answer and worked solution →The number of one-one functions from $\{1,2\}$ to $\{a,b,c\}$ is:Read the answer and worked solution →For functions $f$ and $g$, the composition $(g\circ f)(x)$ means:Read the answer and worked solution →If $f(x) = 2x$ and $g(x) = x + 1$, then $(g\circ f)(x)$ equals:Read the answer and worked solution →A function is invertible if and only if it is:Read the answer and worked solution →The number of bijective functions from a set with $n$ elements onto itself is:Read the answer and worked solution →

Worked practice questions

How many perfect cubes are there from 1 to 1000 (both included)?

  1. 8
  2. 9
  3. 10
  4. 20
Show answer and solution

Correct answer: C. 10

The cubes from 1 to 1000 are 1³, 2³, 3³, …, 10³ = 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. That is exactly 10 perfect cubes in this range.

Open this question →

What is the cube of 12?

  1. 144
  2. 1278
  3. 1728
  4. 2178
Show answer and solution

Correct answer: C. 1728

12³ = 12 × 12 × 12 = 144 × 12 = 1728. (1728 is also notable as 1 + 1728 = 1729, the Hardy-Ramanujan number.)

Open this question →

Which of the following numbers is NOT a perfect cube?

  1. 216
  2. 512
  3. 1000
  4. 100
Show answer and solution

Correct answer: D. 100

216 = 6³, 512 = 8³, 1000 = 10³ — all perfect cubes. 100 is between 4³ = 64 and 5³ = 125, so it is NOT a perfect cube.

Open this question →

How to practise

  1. Choose a Unit 1A1: Relations, Functions and Graphs question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Unit 1A1: Relations, Functions and Graphs practice for GRE. Read explanations as you go. No signup form needed to start.

Practise Unit 1A1: Relations, Functions and Graphs →

More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits